How should I patch this large, odd-shaped hole?

This is a hole the plumber left and I would like to patch this myself.

It's my first time patching drywall but I figured since it's in the garage, it's fine if it looks terrible but will be good practice for when I decide to patch walls up inside my house.

I have a few questions:

1. Should I do this in several pieces or should I cut out one large piece of drywall to fit?

2. The original wall seems to be in two layers. What thickness of drywall should I use? Should I use two layers? If so, do I install them one at a time or do it the same time?

3. How do I anchor it to the door frame?